having trouble with this question:
Given that p and q are real and that 1 + 2i is a root of this equation:
z^2 + (p+5i)*z +q(2 - i) = 0
- Determine the values of p and q
- Determine the other root of the equation
I really have no idea how to approach this.
Hi plato - should that expansion not be (p + 2q - 13) + i(2p -q +9).
I'm still at a loss - I thought it would be solved by comparing the original equation to (x - α) (x - β). After expanding with replacing with the root and its conjugate fianlly compare the coefficiants.
I then get p = -2 -5i and q = 2 + i
Your expansion is correct. But since you're told that p and q are real it is unlikely that your answers are correct ....
Did you equate the real and imaginary parts of the expanded expression to zero and solve the resulting two equations simultaneously (as advised by Plato)? If so, please show your work.